Chapter 6: Fractions – Exercise 6.7
Question: 1
Write each fraction. Arrange them in ascending and descending order using correct sign ‘ < ‘ , ‘ = ‘ > ‘ between the fractions:
Solution:
Question: 2
Mark 2/6,4/6, 8/6, 6/6 on the number line and put appropriate signs between fractions given below:
Solution:
i) 56 > 26 because 5 > 2 and the denominator is the same.
ii) 36 > 06 because 3 > 0 and the denominator is the same.
iii) 16 < 66 because 6 > 1 and the denominator is the same.
iv) 86 > 56 because 8 > 5 and the denominator is the same.
Question: 3
Compare the following fractions and put an appropriate:
Solution:
i) 36 < 56 because 3 < 5 and the denominator is the same.
ii) 45 > 05 because 4 > 0 and the denominator is the same.
iii) 320 < 420 because 3 < 4 and the denominator is the same.
iv) 17 < 14 because 7 > 4; if the numerator is the same, then the fraction that has smaller denominator is greater.
Question: 4
Compare the following fractions using the symbol > or <:
i) 6/7 and 6/11
ii) 3/7 and 5/7
iii) 2/3 and 8/12
iv) 1/5 and 4/15
v) 8/3 and 8/13
vi) 4/9 and 15/8
Solution:
i) 6/7 > 6/11 because if the numerator is the same, then the fraction with smaller denominator is greater.
ii) 3/7 < 5/7 because 3 < 5 and the denominator is the same.
(Because 3 < 4 and the denominator is the same. Therefore, 1/15 < 4/15)
v) 8/3 < 8/13 Because if the numerator is the same, then the fraction with smaller denominator is greater.
(Because 135 > 32 and the denominator is the same)
Therefore, 4/9 < 15/8
Question: 5
The following fractions represent just three different numbers. Separate them in to three groups of equal fractions by changing each one to its simplest form:
i) 2/12
ii) 3/15
iii) 8/50
iv) 16/100
v) 10/60
vi) 15/75
vii) 12/60
viii) 16/96
ix) 12/75
x) 12/72
xi) 3/18
xii) 4/25
Solution:
i) 2/12
HCF of 2 & 12 is 2.
Divide both the numerator & denominator by the HCF of 2 &12
ii) 3/15
HCF of 3 & 15 is 3.
Divide both the numerator & denominator by the HCF of 3 &15.
iii) 8/50
HCF of 8 & 50 is 2.
Divide both the numerator & denominator by the HCF of 8 & 50.
iv) 16/100
HCF of 16 & 100 is 4.
Divide both the numerator & denominator by the HCF of 16 & 100.
v) 10/60
HCF of 10 & 60 is 10.
Divide both the numerator & denominator by the HCF of 10 & 60.
vi) 15/75
HCF of 15 & 75 is 15.
Divide both the numerator & denominator by the HCF of 15 & 75.
vii) 12/60
HCF of 12 & 60 is 12.
Divide both the numerator & denominator by the HCF of 12 & 60.
viii) 16/96
HCF of 16 & 96 is 16.
Divide both the numerator & denominator by the HCF of 16 & 96
ix) 12/75
HCF of 12 & 75 is 3.
Divide both the numerator & denominator by the HCF of 12 & 75.
x) 12/72
HCF of 12 & 72 is 12.
Divide both the numerator & denominator by the HCF of 12 & 72
xi) 3/18
HCF of 3 & 18 is 3.
Divide both the numerator & denominator by the HCF of 3 & 18.
xii) 4/25
HCF of 4 & 25 is 1.
Divide both the numerator & denominator by the HCF of 4 & 25
Three groups of equal fractions:
Question: 6
Isha read 25 pages of a book containing 100 pages. Nagma read 1/2 of the same book. Who read less?
Solution:
Total pages in the book = 100
(Dividing numerator & denominator by the HCF of 25 & 100)
Fraction of the book read by Nagma = 12
Now, compare 14 & 12.
LCM of 4 & 2 is 4.
Convert each fraction into equivalent fraction with 4 as its denominator.
Therefore, Isha read less.
Question: 7
Arrange the following fractions in the ascending order:
Solution:
i) 2/9, 7/9, 3/9, 4/9, 1/9, 6/9, 5/9, when the denominators are the same and numerators are different, then the fraction with greater numerator has a larger value.
ii) 7/8, 7/25, 7/11, 7/18, 7/10, when numerator are the same and denominators are different, the fraction with greater denominator has a smaller value.
iii) 37/47, 37/50, 37/100, 37/100, 37/85, 37/41
When numerators are the same and denominator has a smaller value.
iv) 3/5, 1/5, 4/5, 2/5
When denominators are the same and numerators are different, then the fraction with greater numerator has a larger value.
v) LCM of 2, 4 and 5 is 20
vi) 3/12, 3/8, 3/6, 3/4.
vii) 5/16, 3/8, 6/12, 4/6
Question: 8
Arrange in descending order in each of the following using symbols >:
i) 8/17, 8/9, 8/5, 8/13
ii) 5/9, 3/12, 1/3, 4/15
Solution:
i) 8/5 > 8/9 > 8/13 > 8/17
ii) 5/9 > 1/3 > 3/12 > 4/15
Question: 9
Find answers to the following. Write and indicate how you solved them.
i) Is 5/9 equal to 4/5?
ii) Is 9/16 equal to 5/9?
iii) Is 4/5 equal to 16/20?
iv) Is 1/15 equal to 4/30?
Solution:
i) No. 5 × 5 ≠ 9 × 4
ii) No. 9 × 9 ≠ 16 × 5
iii) yes. 4 × 20 = 16 × 5
iv) No. 1 × 30 = 15 × 4